Question

define f : X → Y, g : Y → Z and h : Y → Y

Answer 1

$f:X \rightarrow Y$ defines that f is function which takes in the value from the set of X and return the values from the set of Y.

For example: $f(x)=x^2$

This function takes in the value from the set of all real numbers but returns the value from the set of all positive numbers.

Similarly, $g:Y\rightarrow Z$ defines that g is function which takes in the value from the set of Y and return the values from the set of Z.

For example: $g(x)=-\sqrt{x}$

This function takes in the value from the set of all positive numbers but returns the value from the set of all negative numbers.

Similarly, $h:Y\rightarrow Y$ defines that h is a function which takes in the value from the set of Y and also returns the values from the set of Y.

For example: $h(x)=\sqrt{x}$

This function takes in the value from the set of all positive numbers and also returns the value from the set of all positive numbers.